Edit mode object mesh offset? Not sure how to explain this
It looks to me like you have an un-applied sub-surface (subsurf) modifier assigned to the object. The solid part is the representation of what the object looks like with the subsurf, but since it is not applied, the solid part is not directly editable in edit mode. If you move some of the vertices you can edit, you will find that the solid surface moves, too. An additional clue that this is the case is the normal lines pointing from each face.